Exact module categories over $\mathrm{Rep}(u_q({\mathfrak{sl}}_2))$

Abstract

We give a complete list of indecomposable exact module categories over the finite tensor category $\mathrm{Rep}(u_q({\mathfrak{sl}}_2))$ of representations of the small quantum group $u_q({\mathfrak{sl}}_2)$, where $q$ is a root of unity of odd order. Each of them is given as the category of representations of a left comodule algebra over $u_q({\mathfrak{sl}}_2)$ explicitly presented by generators and relations.

49 pages